Problem: Solve the system of equations. $\begin{aligned} & 8x+5y = 24 \\\\ & y=-4x \end{aligned}$ $ x=$
Solution: We are given that $ y = {-4x}$. Let's substitute this expression into the first equation and solve for $x$ as follows: $\begin{aligned} 8x+5{y}&=24\\\\ 8x+5\cdot({-4x})&=24\\\\ 8x-20x& = 24\\\\ -12x&=24\\\\ x&=-2 \end{aligned}$ Since we now know that $ x={-2}$, we can substitute this value into the second equation to solve for $y$ as follows: $\begin{aligned} y &= -4{x} \\\\ y&=-4\cdot({-2})\\\\ y&=8 \end{aligned}$ This is the solution of the system: $\begin{aligned} &x = -2 \\\\ &y=8 \end{aligned}$